Below are some examples based on the data to demonstrate the use of the formulas.

Example 1.

Calculating the Standard Error from the Confidence Interval
The estimated number of never married males is 34,171,130. This information comes from summary table B12001 for the United States for 2005. The margin of error is 81,645.

Standard Error = Margin of Error / 1.645

Calculating the standard error using the margin of error, we have:

SE(34,171,130) = 81,645 / 1.645 = 49,632.

Example 2.

Calculating the Standard Error of a Sum or Difference
We are interested in the total number of people who have never been married. From Example 1, we know the number of never married males is 34,171,130. From summary table B12001 the number of never married females is 29,943,646 with a margin of error of 74,944. Combining these two estimates, the estimated number of people who have never been married is 64,114,776. To calculate the standard error of this sum, we need the standard errors of the two estimates that comprise the sum. From Example 1, the standard error for the number of never married males is 49,632. The standard error for the number of never married females is calculated the same way as in Example 1, using the margin of error:
SE(29,943,646) = 74,944 / 1.645 = 45,559.

The formula for the standard error of a sum or difference is:

Using the formula for the standard error of a sum or difference, we have:

In order to calculate the margin of error at the 90 percent confidence interval for the estimate of people who have never been married, we reverse the process in Example 1.

Margin of Error = Standard Error * 1.645

Calculating the margin of error using the standard error, we have:

ME(64,114,776) = 67,372 * 1.645 = 110,827

The margin of error for the estimate of people who have never been married is
(+/-) 110,827.

Example 3.

Calculating the Standard Error of a Proportion or Percent
We are interested in looking at the proportion of females who have never been married. As shown in Example 2, the number of never married females is 29,943,646. In order to calculate the percentage, we also need to know the number of people who have never been married (64,114,776).
The estimate is (29,943,646 / 64,114,776) = 0.467
0.467 is the proportion of the never married population that is women. To convert this to a percent, multiply the proportion by 100.
To calculate the standard error of this sum, we need the standard errors of the two estimates in the sum. Getting this information from Example 2, the standard error for the number of never married females is 45,559 and the standard error for the number of never married people is 67,372.
The formula for the standard error of a proportion or percent is:

To calculate the margin of error at the 90 percent confidence interval around 0.467 using the standard error, we follow the same formula detailed in Example 2.
ME(0.467) = 0.0005 * 1.645 = 0.000825
The margin of error for the estimate of proportion of females who have never been married is (+/-) 0.000825.

Users should be cautioned that all methods in this section are approximations. They may be overestimates or underestimates of the estimate's standard error, and may not match direct calculations of standard errors or calculations obtained through other methods.
For more detailed information on the calculations of standard errors and the reasoning for the formulas please reference the Accuracy of the Data Document located on the following URL: http://www.census.gov/acs/www/UseData/Accuracy/Accuracy1.htm